Contents
Preface ........................................................VII
1 Hello World: Introducing Spatial Data .................... 1
1.1 AppliedSpatialDataAnalysis ............................ 1
1.2 Why Do We Use R ...................................... 2
1.2.1 ... InGeneral? .................................... 2
1.2.2 ... forSpatialDataAnalysis? ....................... 3
1.3 R andGIS.............................................. 4
1.3.1 What isGIS?..................................... 4
1.3.2 Service-Oriented Architectures . . . . . . . . . . . . . . . . . . . . . . 6
1.3.3 Further Reading on GIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 TypesofSpatialData.................................... 7
1.5 StorageandDisplay ..................................... 10
1.6 AppliedSpatialDataAnalysis ............................ 11
1.7 R Spatial Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.7.1 OnlineResources.................................. 14
1.7.2 Layoutof theBook................................ 14
Part I Handling Spatial Data in R
2 Classes for Spatial Data in R .............................. 21
2.1 Introduction ............................................ 21
2.2 Classes and Methods in R ................................ 23
2.3 Spatial Objects ........................................ 28
2.4 SpatialPoints ......................................... 30
2.4.1 Methods ......................................... 31
2.4.2 DataFrames forSpatialPointData ................. 33
2.5 SpatialLines .......................................... 38X Contents
2.6 SpatialPolygons ....................................... 41
2.6.1 SpatialPolygonsDataFrame Objects ................ 44
2.6.2 HolesandRingDirection........................... 46
2.7 SpatialGrid and SpatialPixel Objects................... 47
3 Visualising Spatial Data ................................... 57
3.1 The Traditional Plot System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.1.1 Plotting Points, Lines, Polygons, and Grids . . . . . . . . . . . 58
3.1.2 AxesandLayoutElements ......................... 60
3.1.3 Degrees in Axes Labels and Reference Grid . . . . . . . . . . . 64
3.1.4 Plot Size, Plotting Area, Map Scale,
and Multiple Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.1.5 Plotting Attributes and Map Legends . . . . . . . . . . . . . . . . 66
3.2 Trellis/Lattice Plots with spplot .......................... 68
3.2.1 A Straight Trellis Example . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.2 Plotting Points, Lines, Polygons, and Grids . . . . . . . . . . . 70
3.2.3 Adding Reference and Layout Elements to Plots . . . . . . 72
3.2.4 Arranging Panel Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.3 Interacting with Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.3.1 InteractingwithBaseGraphics...................... 74
3.3.2 Interacting with spplot and Lattice Plots . . . . . . . . . . . . 76
3.4 ColourPalettesandClass Intervals ........................ 76
3.4.1 ColourPalettes ................................... 76
3.4.2 Class Intervals .................................... 77
4 Spatial Data Import and Export ........................... 81
4.1 CoordinateReferenceSystems ............................ 82
4.1.1 Using the EPSG List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.1.2 PROJ.4 CRS Specification. . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.1.3 ProjectionandTransformation...................... 85
4.1.4 Degrees, Minutes, and Seconds . . . . . . . . . . . . . . . . . . . . . . 87
4.2 Vector File Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
4.2.1 Using OGR Drivers in rgdal . . . . . . . . . . . . . . . . . . . . . . . . 89
4.2.2 Other Import/ExportFunctions..................... 93
4.3 Raster File Formats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3.1 Using GDAL Drivers in rgdal . . . . . . . . . . . . . . . . . . . . . . . 94
4.3.2 Writing a Google Earth™ ImageOverlay ............. 97
4.3.3 Other Import/ExportFunctions..................... 98
4.4 Grass .................................................. 99
4.4.1 BroadStreetCholeraData .........................104
4.5 Other Import/Export Interfaces ...........................106
4.5.1 Analysis and Visualisation Applications . . . . . . . . . . . . . . 108
4.5.2 TerraLibandaRT.................................108
4.5.3 OtherGISandWebMappingSystems ...............110
4.6 Installing rgdal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111Contents XI
5 Further Methods for Handling Spatial Data ...............113
5.1 Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.2 Overlay ................................................116
5.3 Spatial Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5.4 Checking Topologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.4.1 Dissolving Polygons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.4.2 Checking Hole Status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.5 Combining Spatial Data ..................................123
5.5.1 Combining Positional Data . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.5.2 Combining Attribute Data . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.6 Auxiliary Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6 Customising Spatial Data Classes and Methods ............127
6.1 Programming with Classes and Methods . . . . . . . . . . . . . . . . . . . 127
6.1.1 S3-StyleClassesandMethods.......................129
6.1.2 S4-StyleClassesandMethods.......................130
6.2 AnimalTrackDatainPackageTrip........................130
6.2.1 GenericandConstructorFunctions ..................131
6.2.2 Methods forTripObjects ..........................133
6.3 Multi-Point Data: SpatialMultiPoints ....................134
6.4 Hexagonal Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
6.5 Spatio-Temporal Grids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
6.6 Analysing Spatial Monte Carlo Simulations . . . . . . . . . . . . . . . . . 144
6.7 Processing Massive Grids . ................................146
Part II Analysing Spatial Data
7 Spatial Point Pattern Analysis .............................155
7.1 Introduction ............................................155
7.2 Packages for the Analysis of Spatial Point Patterns . . . . . . . . . . 156
7.3 Preliminary Analysis of a Point Pattern . . . . . . . . . . . . . . . . . . . . 160
7.3.1 CompleteSpatialRandomness ......................160
7.3.2 G Function: Distance to the Nearest Event . . . . . . . . . . . 161
7.3.3 F Function: Distance from a Point
totheNearestEvent...............................162
7.4 Statistical Analysis of Spatial Point Processes . . . . . . . . . . . . . . . 163
7.4.1 Homogeneous Poisson Processes . . . . . . . . . . . . . . . . . . . . . 164
7.4.2 Inhomogeneous Poisson Processes . . . . . . . . . . . . . . . . . . . 165
7.4.3 Estimationof theIntensity .........................165
7.4.4 Likelihood of an Inhomogeneous Poisson Process . . . . . . 168
7.4.5 Second-Order Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
7.5 Some Applications in Spatial Epidemiology . . . . . . . . . . . . . . . . . 172
7.5.1 Case–Control Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
7.5.2 Binary Regression Estimator . . . . . . . . . . . . . . . . . . . . . . . . 178XII Contents
7.5.3 Binary Regression Using Generalised
Additive Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.5.4 Point Source Pollution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
7.5.5 Accounting for Confounding and Covariates . . . . . . . . . . 186
7.6 Further Methods for the Analysis of Point Patterns . . . . . . . . . . 190
8 Interpolation and Geostatistics ............................191
8.1 Introduction ............................................191
8.2 Exploratory Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
8.3 Non-Geostatistical InterpolationMethods ..................193
8.3.1 InverseDistanceWeightedInterpolation..............193
8.3.2 Linear Regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
8.4 Estimating Spatial Correlation: The Variogram. . . . . . . . . . . . . . 195
8.4.1 Exploratory Variogram Analysis . . . . . . . . . . . . . . . . . . . . . 196
8.4.2 Cutoff,LagWidth,DirectionDependence ............200
8.4.3 Variogram Modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
8.4.4 Anisotropy .......................................205
8.4.5 Multivariable Variogram Modelling . . . . . . . . . . . . . . . . . . 206
8.4.6 Residual Variogram Modelling . . . . . . . . . . . . . . . . . . . . . . 208
8.5 SpatialPrediction .......................................209
8.5.1 Universal, Ordinary, and Simple Kriging . . . . . . . . . . . . . 209
8.5.2 Multivariable Prediction: Cokriging . . . . . . . . . . . . . . . . . . 210
8.5.3 Collocated Cokriging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
8.5.4 Cokriging Contrasts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
8.5.5 Kriging in a Local Neighbourhood . . . . . . . . . . . . . . . . . . . 213
8.5.6 Change of Support: Block Kriging . . . . . . . . . . . . . . . . . . . 215
8.5.7 Stratifying the Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
8.5.8 TrendFunctionsandtheirCoefficients ...............217
8.5.9 Non-Linear Transforms of the Response Variable . . . . . . 218
8.5.10 Singular Matrix Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
8.6 ModelDiagnostics.......................................221
8.6.1 Cross Validation Residuals . . . . . . . . . . . . . . . . . . . . . . . . . 222
8.6.2 Cross Validation z-Scores...........................223
8.6.3 Multivariable Cross Validation . . . . . . . . . . . . . . . . . . . . . . 225
8.6.4 Limitations to Cross Validation . . . . . . . . . . . . . . . . . . . . . 225
8.7 GeostatisticalSimulation.................................226
8.7.1 SequentialSimulation..............................227
8.7.2 Non-Linear Spatial Aggregation and Block Averages . . . 229
8.7.3 Multivariable and Indicator Simulation . . . . . . . . . . . . . . . 230
8.8 Model-Based Geostatistics and Bayesian Approaches . . . . . . . . . 230
8.9 MonitoringNetworkOptimization .........................231
8.10 Other R Packages for Interpolation and Geostatistics . . . . . . . . . 233
8.10.1 Non-Geostatistical Interpolation.....................233
8.10.2 spatial ...........................................233
8.10.3 RandomFields ....................................234
8.10.4 geoRandgeoRglm ................................235
8.10.5 fields ............................................235Contents XIII
9 Areal Data and Spatial Autocorrelation ...................237
9.1 Introduction ............................................237
9.2 SpatialNeighbours ......................................239
9.2.1 NeighbourObjects ................................240
9.2.2 Creating Contiguity Neighbours . . . . . . . . . . . . . . . . . . . . . 242
9.2.3 CreatingGraph-BasedNeighbours...................244
9.2.4 Distance-BasedNeighbours .........................246
9.2.5 Higher-OrderNeighbours...........................249
9.2.6 Grid Neighbours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250
9.3 SpatialWeights .........................................251
9.3.1 SpatialWeightsStyles .............................251
9.3.2 GeneralSpatialWeights............................253
9.3.3 Importing, Converting, and Exporting Spatial
NeighboursandWeights ...........................255
9.3.4 Using Weights to Simulate Spatial Autocorrelation . . . . 257
9.3.5 Manipulating Spatial Weights . . . . . . . . . . . . . . . . . . . . . . . 258
9.4 SpatialAutocorrelation:Tests.............................258
9.4.1 GlobalTests......................................261
9.4.2 LocalTests .......................................268
10 Modelling Areal Data .....................................273
10.1 Introduction ............................................273
10.2 SpatialStatisticsApproaches .............................274
10.2.1 Simultaneous Autoregressive Models . . . . . . . . . . . . . . . . . 277
10.2.2 Conditional Autoregressive Models . . . . . . . . . . . . . . . . . . 282
10.2.3 Fitting Spatial Regression Models . . . . . . . . . . . . . . . . . . . 284
10.3 Mixed-Effects Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
10.4 Spatial Econometrics Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 289
10.5 OtherMethods..........................................296
10.5.1 GAM, GEE, GLMM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
10.5.2 MoranEigenvectors ...............................302
10.5.3 Geographically Weighted Regression . . . . . . . . . . . . . . . . . 305
11 Disease Mapping ..........................................311
11.1 Introduction ............................................312
11.2 StatisticalModels .......................................314
11.2.1 Poisson-GammaModel.............................315
11.2.2 Log-NormalModel ................................316
11.2.3 Marshall’s Global EB Estimator . . . . . . . . . . . . . . . . . . . . . 318
11.3 SpatiallyStructuredStatisticalModels.....................319
11.4 BayesianHierarchicalModels .............................321
11.4.1 ThePoisson-GammaModelRevisited................322
11.4.2 SpatialModels....................................325
11.5 DetectionofClustersofDisease ...........................332
11.5.1 Testing the Homogeneity of the Relative Risks . . . . . . . . 333
11.5.2 Moran’s I TestofSpatialAutocorrelation ............335XIV Contents
11.5.3 Tango’sTestofGeneralClustering ..................335
11.5.4 Detection of the Location of a Cluster . . . . . . . . . . . . . . . 337
11.5.5 GeographicalAnalysisMachine .....................337
11.5.6 Kulldorff’s Statistic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338
11.5.7 Stone’sTest forLocalisedClusters...................340
11.6 OtherTopics inDiseaseMapping..........................341
Afterword .....................................................343
R andPackageVersionsUsed..................................344
DataSetsUsed..............................................344
References .....................................................347
Subject Index .................................................361
Functions Index ...............................................371
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